Six Women in a Hotel

Logic
Logic puzzles require you to think. You will have to be logical in your reasoning.

Audrey, Brenda, Charlotte, Dawn, Edith, and Fran stayed in a hotel. Each stayed in a different room:

Audrey's room was large and bordered Brenda, Charlotte, Dawn, and Fran.
Brenda's room was medium and bordered Audrey and Charlotte.
Charlotte's room was small and bordered Audrey, Brenda, and Dawn.
Dawn's room was medium and bordered Audrey, Charlotte, Edith, and Fran.
Edith's room was small and bordered Dawn and Fran.
Fran's room was large and bordered Audrey, Dawn, and Edith.

One of the six murdered one of the other five. Here are some facts:

1. If the murderer's room and the victim's room did not border each other, the victim was either Audrey or Fran.

2. If the murderer's room and the victim's room bordered different numbers of rooms, the murderer was either Brenda or Charlotte.

3. If the murderer's room and the victim's room were different sizes, the murderer was either Dawn or Edith.

Who was the murderer?

Hint

All three facts are in the form of hypothesis and conclusion statements. If the hypothesis of such a statement is false, or if the conclusion is true, the full statement is true. Otherwise, the statement is false.

Answer

Dawn was the murderer.

Since there was only one murderer, conclusions 2 and 3 cannot be true at the same time, and therefore at least one of these conclusions must be false. This means that at least one hypothesis must be false.

Notice how no two rooms of the same size border the same number of rooms. This means that one of hypotheses 2 and 3 is true, and the other is false.

If hypothesis 2 is true and hypothesis 3 is false, then the two rooms are the same size, and the murderer is Brenda or Charlotte. If the murderer is Brenda, the victim is Dawn. If the murderer is Charlotte, the victim is Edith. But both situations contradict fact 1.

This means that hypothesis 2 is false, hypothesis 3 is true, the two rooms border the same number of rooms, and the murderer was either Dawn or Edith. If the murderer was Edith, the victim was Brenda, which contradicts fact 1. This means the murderer was Dawn, and her victim was Audrey. And since hypotheses 1 and 2 are false, and since conclusions 1 and 3 are true, this gives us no contradictions.